Suppose ψ(adsbygoogle = window.adsbygoogle || []).push({}); _{1}and ψ_{2}are two eigenfunctions of a particle and ε_{1}and ε_{2}are the corresponding eigenvalues. If the state is in the superposition Ψ = αψ_{1}+ βψ_{2}at time t=0, it evolves in time by the equation Ψ = αψ_{1}e^{i ħ/ε1 t}+ βψ_{2}e^{i ħ/ε2 t}. I am trying to understand the probability amplitude Ψ*Ψ.If you take Ψ* and multiply with Ψ in the cross terms of ψ_{1}and ψ_{2}there will be the exponential part containing the imaginary component i. How is this possible? Shouldnt the probability function, being the square of the wave function always be real so that we have measurable quantity associated with the wave function? If the probability function stops being real, what does that mean in the real world? Thanks!!!

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# Probability function being imaginary?

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